{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Welcome to the DL in Inverse Scattering Tutorial. Through this notebook, we aim to provide a step-by-step introduction to codes used in implemenation of the scheme provided in <i>Embedding Deep Learning in Inverse Scattering Problem</i>. After going through this notebook, one can perform the numerical experiments themselves to generate the results presented in our aforementioned paper. \n",
    "\n",
    "The link to original paper can be found <a href = \"https://ieeexplore.ieee.org/document/8709721\">here</a>. We have also provided a link to slides of corresponding conference paper presented at URSI-APRASC 2019 Delhi <a href=\"https://sanghviyashiitb.github.io/blog/2019-3-31-URSI\">here</a>.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To start off, we firstly need to initialize some problem parameters. Since our scheme is heavily using Subspace Optimization Method (SOM), we use the parameters as ones used in the original SOM paper i.e. <a href = \"https://ieeexplore.ieee.org/abstract/document/5210141\">Subspace-Based Optimization Method for Solving Inverse-Scattering Problems</a>.\n",
    "\n",
    "The imaging domain, $D$, is assumed to be of size $2m \\times 2m$ and the object of interest is located within this domain. The incident field is $400MHz$, and hence the free space wavelength is $\\lambda = 0.75m$. The measurements are taken on a circle of radius $R_S = 4m$ with the centre of the circle coinciding with the center of $D$ and $N_s = 32$ receivers are placed along the measurement domain in an equiangular manner for each illuminations. Total number of different illuminations are $N_I = 16$ and the corresponding transceivers are placed on the radius $R_i = 6m$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.insert(0, './utility/')\n",
    "sys.path.insert(0, './SOM_CSI/')\n",
    "import numpy as np\n",
    "import generate_shapes\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Frequency = 400MHz\n",
    "f = 4e8\n",
    "wavelength = 3e8/f\n",
    "\n",
    "# k := Wavenumber\n",
    "k = 2*np.pi/wavelength \n",
    "\n",
    "# d := Dimension of imaging domain D in meters\n",
    "d = 2 \n",
    "\n",
    "# R := Radius of measurement domain\n",
    "R = 4\n",
    "\n",
    "# M := Number of Receivers per illumination\n",
    "M = 32\n",
    "\n",
    "# V := Number of illuminations\n",
    "V = 16"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given these paramters, we can generate other quantities such as positions of discretized grids, receivers and transceivers. Additionally, we also need the incident field vector for the inverse scattering problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import setup_functions\n",
    "\n",
    "# The imaging domain is discretized into L X L cells\n",
    "L = 32 \n",
    "# Dimension of one cell\n",
    "n = d/L \n",
    "# Number of pixels\n",
    "N = L^2\n",
    "\n",
    "# Positions of center of each grid. Shape = [N, 2]\n",
    "# pos_D[i,:] = [x coordinate, y coordinate] of cell #i \n",
    "pos_D = setup_functions.gen_pos_D(d,L,n)\n",
    "\n",
    "# Positions of Receivers and Transceivers. Shape = [M,2] and [V,2] respectively\n",
    "# pos_S[i,:] = [x coordinate, y coordinate] of receiver #i \n",
    "pos_S = setup_functions.gen_pos_S(R, M, d) \n",
    "# pos_Tx[i,:] = [x coordinate, y coordinate] of transceiver #i \n",
    "pos_Tx = setup_functions.gen_pos_Tx(R*1.5, V, d)\n",
    "\n",
    "# Incident Field, Shape = [N,1] (Complex vector)\n",
    "e = setup_functions.gen_e(k, pos_D, pos_Tx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need the scattered fields which will be used to obtain the dielectric profile. In absence of actual data, we simulate the experimental data by running the forward solver at a higher resolution ($L = 100$) in this case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For forward solver\n",
    "L_forward = 32\n",
    "n_forward = d/L_forward\n",
    "\n",
    "pos_D_forward = setup_functions.gen_pos_D(d,L_forward,n_forward)\n",
    "e_forward = setup_functions.gen_e(k, pos_D_forward, pos_Tx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the CG-FFT forward solver to find out the internal fields and then calculate the scattered fields at external points using the matrix $G_S$. The process can be summarized as follows:\n",
    "$$d_n =  e_n + G_DXe_n$$\n",
    "$$\\Rightarrow w_n = Xe_n + XG_Dw_n$$\n",
    "$$ s_n = G_S w_n $$\n",
    "\n",
    "Note that the symbols used have the same meaning as those defined in our paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/fftpack/basic.py:160: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  z[index] = x\n"
     ]
    }
   ],
   "source": [
    "import util_cgfft\n",
    "import util_functions\n",
    "# Forward Solver parameters for L = 100 \n",
    "# FFT representation of G_D matrix\n",
    "g_D_forward, g_D_fft_forward, g_D_fft_conj_forward = util_cgfft.construct_g_D(pos_D_forward, k, n_forward)\n",
    "\n",
    "# G_S matrix for forward solver\n",
    "G_S_forward = util_functions.construct_G_S(pos_D_forward, pos_S, k, n_forward)\n",
    "\n",
    "# Forward Solver parameters for L = 32 \n",
    "G_D = util_functions.construct_G_D(pos_D, k, n)\n",
    "# FFT representation of G_D matrix\n",
    "g_D, g_D_fft, g_D_fft_conj = util_cgfft.construct_g_D(pos_D, k, n)\n",
    "\n",
    "# G_S matrix for inverse solver solver\n",
    "G_S = util_functions.construct_G_S(pos_D, pos_S, k, n)\n",
    "\n",
    "\n",
    "############################################################# \n",
    "# Generating parameters for Inversion at 16 X 16 Resolution\n",
    "#############################################################\n",
    "L1 = 16\n",
    "n_L1 = d/L1\n",
    "\n",
    "pos_D_L1 = setup_functions.gen_pos_D(d,L1,n_L1)\n",
    "e_L1 = setup_functions.gen_e(k, pos_D_L1, pos_Tx)\n",
    "\n",
    "g_D_L1, g_D_fft_L1, g_D_fft_conj_L1 = util_cgfft.construct_g_D(pos_D_L1, k, n_L1)\n",
    "G_S_L1 = util_functions.construct_G_S(pos_D_L1, pos_S, k, n_L1)\n",
    "G_D_L1 = util_functions.construct_G_D(pos_D_L1, k, n_L1)\n",
    "\n",
    "## Ignore the warning which comes after running the code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But what object we are going to run the forward solver on? We use the Austria profile which is often used to validate inverse scattering algorithms. However, we increase the contrast of the profile to make an electrically stronger object for which conventional algorithms fail"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x111d26ac8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "max_contrast = 4.0\n",
    "x_au = generate_shapes.austria_multicontrast(L_forward,max_contrast,max_contrast,max_contrast)\n",
    "\n",
    "# Display Austria Profile\n",
    "plt.imshow(np.real(x_au))\n",
    "plt.xticks([L_forward*0.25, L_forward*0.5, L_forward*0.75], [-0.5, 0, 0.5],fontsize = '16')\n",
    "plt.yticks([L_forward*0.25, L_forward*0.5, L_forward*0.75], [-0.5, 0, 0.5],fontsize = '16')\n",
    "plt.xlabel('x (in m)', fontsize='16')\n",
    "plt.ylabel('y (in m)', fontsize='16')\n",
    "plt.title('Austria Profile', fontsize='18')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CG-FFT solver is used to generate scattered field data which will be later used in the inversion process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Forward Solver for 16 illuminations\n",
      "This might take a while...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/fftpack/basic.py:160: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  z[index] = x\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tolerance = 0.430e-6 at iteration = 210 for 1th illumination\n",
      "Tolerance = 0.873e-6 at iteration = 216 for 2th illumination\n",
      "Tolerance = 0.536e-6 at iteration = 218 for 3th illumination\n",
      "Tolerance = 0.153e-6 at iteration = 217 for 4th illumination\n",
      "Tolerance = 0.584e-6 at iteration = 122 for 5th illumination\n",
      "Tolerance = 0.129e-6 at iteration = 216 for 6th illumination\n",
      "Tolerance = 0.630e-6 at iteration = 221 for 7th illumination\n",
      "Tolerance = 0.285e-6 at iteration = 218 for 8th illumination\n",
      "Tolerance = 0.739e-6 at iteration = 212 for 9th illumination\n",
      "Tolerance = 0.130e-6 at iteration = 220 for 10th illumination\n",
      "Tolerance = 0.560e-6 at iteration = 226 for 11th illumination\n",
      "Tolerance = 0.667e-6 at iteration = 215 for 12th illumination\n",
      "Tolerance = 0.835e-6 at iteration = 122 for 13th illumination\n",
      "Tolerance = 0.714e-6 at iteration = 213 for 14th illumination\n",
      "Tolerance = 0.549e-6 at iteration = 215 for 15th illumination\n",
      "Tolerance = 0.438e-6 at iteration = 215 for 16th illumination\n",
      "Completed running the solver.\n"
     ]
    }
   ],
   "source": [
    "# Generating scattered field from profile\n",
    "# Reshape profile into [N,1] vector\n",
    "x = np.reshape(x_au,[L_forward*L_forward,1])\n",
    "# Run the forward solver\n",
    "print('Running Forward Solver for %d illuminations'%(V))\n",
    "print('This might take a while...')\n",
    "y, _ = util_cgfft.cg_fft_forward_problem(x, G_S_forward, g_D_fft_forward, e_forward, 1e-6, e_forward, 1000)\n",
    "# Add 25dB Gaussian Noise\n",
    "print('Completed running the solver.')\n",
    "y = util_functions.add_noise(y, 25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, we try to reconstruct the original profile from scattered field through plain SOM. As we'll see, the reconstruction would fail as the underlying object is too small. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Singular Values used: 20\n",
      "Number of Singular Values used: 20\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/fftpack/basic.py:160: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  z[index] = x\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADMM_Elapsed Time: 0.482\n",
      "Iteration: 0, Cost function: 12.28658\n",
      "SOM Iteration time: 0.671\n",
      "ADMM_Elapsed Time: 0.076\n",
      "Iteration: 1, Cost function: 10.55251\n",
      "SOM Iteration time: 0.286\n",
      "ADMM_Elapsed Time: 0.107\n",
      "Iteration: 2, Cost function: 9.25895\n",
      "SOM Iteration time: 0.354\n",
      "ADMM_Elapsed Time: 0.063\n",
      "Iteration: 3, Cost function: 8.50582\n",
      "SOM Iteration time: 0.297\n",
      "ADMM_Elapsed Time: 0.072\n",
      "Iteration: 4, Cost function: 7.92397\n",
      "SOM Iteration time: 0.287\n",
      "ADMM_Elapsed Time: 0.068\n",
      "Iteration: 5, Cost function: 7.34927\n",
      "SOM Iteration time: 0.284\n",
      "ADMM_Elapsed Time: 0.074\n",
      "Iteration: 6, Cost function: 7.05185\n",
      "SOM Iteration time: 0.286\n",
      "ADMM_Elapsed Time: 0.073\n",
      "Iteration: 7, Cost function: 6.76924\n",
      "SOM Iteration time: 0.278\n",
      "ADMM_Elapsed Time: 0.070\n",
      "Iteration: 8, Cost function: 6.55737\n",
      "SOM Iteration time: 0.279\n",
      "ADMM_Elapsed Time: 0.075\n",
      "Iteration: 9, Cost function: 6.34039\n",
      "SOM Iteration time: 0.287\n",
      "ADMM_Elapsed Time: 0.070\n",
      "Iteration: 10, Cost function: 6.16732\n",
      "SOM Iteration time: 0.274\n",
      "ADMM_Elapsed Time: 0.075\n",
      "Iteration: 11, Cost function: 6.03138\n",
      "SOM Iteration time: 0.281\n",
      "ADMM_Elapsed Time: 0.071\n",
      "Iteration: 12, Cost function: 5.89772\n",
      "SOM Iteration time: 0.271\n",
      "ADMM_Elapsed Time: 0.091\n",
      "Iteration: 13, Cost function: 5.78047\n",
      "SOM Iteration time: 0.330\n",
      "ADMM_Elapsed Time: 0.068\n",
      "Iteration: 14, Cost function: 5.66458\n",
      "SOM Iteration time: 0.345\n",
      "ADMM_Elapsed Time: 0.065\n",
      "Iteration: 15, Cost function: 5.58152\n",
      "SOM Iteration time: 0.459\n",
      "ADMM_Elapsed Time: 0.074\n",
      "Iteration: 16, Cost function: 5.50852\n",
      "SOM Iteration time: 0.326\n",
      "ADMM_Elapsed Time: 0.076\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADMM_Elapsed Time: 0.072\n",
      "Iteration: 921, Cost function: 2.64407\n",
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      "Time elapsed:  317.38625717163086\n"
     ]
    }
   ],
   "source": [
    "############################################# \n",
    "# Running SOM Solver at 32 X 32 Resolution\n",
    "#############################################\n",
    "from SOM import SOM_SingularValues_Morozov, SOM_Stage_II_CGFFT_TV, TSOM_withCGFFT_TV\n",
    "\n",
    "# SVD of G_S, used in extracting row-space components\n",
    "U1, s1, V1h = np.linalg.svd(G_S, full_matrices=False)\n",
    "S1 = np.diag(s1)\n",
    "V1 = V1h.conj().T\n",
    "# Extract row space components from scattered field data\n",
    "w_RS, _ = SOM_SingularValues_Morozov(y, G_S, U1, S1, V1, 25)\n",
    "# Convert w_RS to equivalent contrast\n",
    "d_0 =  e + util_cgfft.G_D_into_x(g_D_fft, w_RS)\n",
    "x_RS = np.reshape( np.sum(d_0.conj()*w_RS, axis = 1)/np.sum(d_0.conj()*d_0,axis=1), (L*L,1) )\n",
    "# Use TSOM+TV to extract the \n",
    "x_L2, _, _ = TSOM_withCGFFT_TV(y, G_S, G_D, g_D_fft, g_D_fft_conj, e, w_RS, 0, False, 500, 2000, 25, 1e-4)\n",
    "x_L2 = np.real(x_L2)*(np.real(x_L2) >= 0) + 1j*np.imag(x_L2)*(np.imag(x_L2) <= 0)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x112429da0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display Reconstruction of Austria Profile\n",
    "plt.imshow(np.real(np.reshape(x_L2,[L,L])))\n",
    "plt.xticks([L*0.25, L*0.5, L*0.75], [-0.5, 0, 0.5],fontsize = '16')\n",
    "plt.yticks([L*0.25, L*0.5, L*0.75], [-0.5, 0, 0.5],fontsize = '16')\n",
    "plt.xlabel('x (in m)', fontsize='16')\n",
    "plt.ylabel('y (in m)', fontsize='16')\n",
    "plt.title('Reconstruction using TSOM+TV', fontsize='18')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As it might be clear from the reconstruction using SOM, Austria contrast 4 profile is too strong an object to recover. The original shape (a ring and 2 disks) is not recovered and the contrast of the reconstructed object is also too low.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our method provides a way to circumvent this issue. The idea is to learn and use the underlying prior of the object to get a better estimate the null subspace of the contrast source. This estimate is further refined by optimizing the cost function used in SOM,by using the null-space estimate as an initialization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To start with, lets obtain the row space coefficient of the contrast source at a 16X16 discretization of the imaging domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Singular Values used: 20\n"
     ]
    }
   ],
   "source": [
    "# SVD of G_S, used in extracting row-space components\n",
    "U1, s1, V1h = np.linalg.svd(G_S_L1, full_matrices=False)\n",
    "S1 = np.diag(s1)\n",
    "V1 = V1h.conj().T\n",
    "\n",
    "# Extract row space components from scattered field data\n",
    "w_RS_L1, _ = SOM_SingularValues_Morozov(y, G_S_L1, U1, S1, V1, 25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a rowspace component, we use a novel convolutional network <i>CS-Net</i> which is trained to predict the noise subspace from the row subspace component of the contrast source. In the following snippet of code, we load a pre-trained CS-Net model and push the signal subspace of the contrast source to it. At the end, we get a prediction of the noise-space. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from ContrastSourceNet import ContrastSourceNet_16_MultiScale_2\n",
    "\n",
    "# Load the trained CS-Net\n",
    "MODEL_L16_FILE = './best_models_yet/ContrastSourceNet_noisydata_25SNR_L16.pth'\n",
    "cs_net = ContrastSourceNet_16_MultiScale_2(V)\n",
    "cs_net.load_state_dict(torch.load(MODEL_L16_FILE))\n",
    "\n",
    "CSImage_input_L1 = np.expand_dims( util_functions.convert_w_to_CSImage(w_RS_L1),axis = 0) \n",
    "CSImage_output_L1 = cs_net( torch.Tensor(CSImage_input_L1) ).detach().numpy()\n",
    "w_DL = util_functions.convert_CSImage_to_w(np.squeeze(CSImage_output_L1, axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total contrast source is used to initialize optimization of the SOM cost function, effectively avoiding the local minima which is often an issue while recovering the electrically strong objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/fftpack/basic.py:160: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  z[index] = x\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Singular Values used: 20\n",
      "Iteration: 0, Cost function: 156.35654\n",
      "SOM Iteration time: 0.063\n",
      "Iteration: 1, Cost function: 120.17980\n",
      "SOM Iteration time: 0.067\n",
      "Iteration: 2, Cost function: 100.53283\n",
      "SOM Iteration time: 0.050\n",
      "Iteration: 3, Cost function: 87.76427\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 4, Cost function: 78.26681\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 5, Cost function: 68.11356\n",
      "SOM Iteration time: 0.056\n",
      "Iteration: 6, Cost function: 59.49542\n",
      "SOM Iteration time: 0.060\n",
      "Iteration: 7, Cost function: 52.29433\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 8, Cost function: 45.73904\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 9, Cost function: 39.87348\n",
      "SOM Iteration time: 0.056\n",
      "Iteration: 10, Cost function: 34.81588\n",
      "SOM Iteration time: 0.058\n",
      "Iteration: 11, Cost function: 30.90071\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 12, Cost function: 28.09392\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 13, Cost function: 26.05341\n",
      "SOM Iteration time: 0.058\n",
      "Iteration: 14, Cost function: 24.31996\n",
      "SOM Iteration time: 0.056\n",
      "Iteration: 15, Cost function: 22.99782\n",
      "SOM Iteration time: 0.059\n",
      "Iteration: 16, Cost function: 21.69565\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 17, Cost function: 20.41434\n",
      "SOM Iteration time: 0.066\n",
      "Iteration: 18, Cost function: 19.30046\n",
      "SOM Iteration time: 0.053\n",
      "Iteration: 19, Cost function: 18.19660\n",
      "SOM Iteration time: 0.061\n",
      "Iteration: 20, Cost function: 17.30253\n",
      "SOM Iteration time: 0.051\n",
      "Iteration: 21, Cost function: 16.57062\n",
      "SOM Iteration time: 0.059\n",
      "Iteration: 22, Cost function: 15.85457\n",
      "SOM Iteration time: 0.054\n",
      "Iteration: 23, Cost function: 15.13547\n",
      "SOM Iteration time: 0.052\n",
      "Iteration: 24, Cost function: 14.39875\n",
      "SOM Iteration time: 0.050\n",
      "Iteration: 25, Cost function: 13.68014\n",
      "SOM Iteration time: 0.057\n",
      "Iteration: 26, Cost function: 13.07663\n",
      "SOM Iteration time: 0.070\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1905, Cost function: 0.18986\n",
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      "Time elapsed:  129.72507882118225\n"
     ]
    }
   ],
   "source": [
    "d_0 =  e_L1 + util_cgfft.G_D_into_x(g_D_fft_L1, w_DL)\n",
    "x_DL = np.reshape( np.sum(d_0.conj()*w_DL, axis = 1)/np.sum(d_0.conj()*d_0,axis=1), (L1*L1,1) )\n",
    "x_DL_SOM, w_DL_SOM, _ = TSOM_withCGFFT_TV(y, G_S_L1, G_D_L1, g_D_fft_L1, g_D_fft_conj_L1, e_L1, w_DL, x_DL, False, 256, 2000, 25, 0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a reconstruction at 16 X 16 pixels, we use it as an initial guess for recovering the contrast profile at a higher (32 X 32) resolution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/fftpack/basic.py:160: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  z[index] = x\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tolerance = 0.660e-3 at iteration = 155 for 1th illumination\n",
      "Tolerance = 0.957e-3 at iteration = 152 for 2th illumination\n",
      "Tolerance = 0.789e-3 at iteration = 156 for 3th illumination\n",
      "Tolerance = 0.411e-3 at iteration = 159 for 4th illumination\n",
      "Tolerance = 0.577e-3 at iteration = 144 for 5th illumination\n",
      "Tolerance = 0.812e-3 at iteration = 145 for 6th illumination\n",
      "Tolerance = 0.642e-3 at iteration = 147 for 7th illumination\n",
      "Tolerance = 0.839e-3 at iteration = 145 for 8th illumination\n",
      "Tolerance = 0.390e-3 at iteration = 161 for 9th illumination\n",
      "Tolerance = 0.382e-3 at iteration = 157 for 10th illumination\n",
      "Tolerance = 0.835e-3 at iteration = 150 for 11th illumination\n",
      "Tolerance = 0.590e-3 at iteration = 161 for 12th illumination\n",
      "Tolerance = 0.388e-3 at iteration = 147 for 13th illumination\n",
      "Tolerance = 0.690e-3 at iteration = 162 for 14th illumination\n",
      "Tolerance = 0.839e-3 at iteration = 158 for 15th illumination\n",
      "Tolerance = 0.312e-3 at iteration = 161 for 16th illumination\n",
      "Number of Singular Values used: 20\n",
      "ADMM_Elapsed Time: 0.103\n",
      "Iteration: 0, Cost function: 108.89045\n",
      "SOM Iteration time: 0.402\n",
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      "Iteration: 1, Cost function: 86.20342\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADMM_Elapsed Time: 0.064\n",
      "Iteration: 1911, Cost function: 3.59333\n",
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      "Iteration: 1944, Cost function: 3.55377\n",
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      "Iteration: 1960, Cost function: 3.53572\n",
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      "Iteration: 1967, Cost function: 3.52819\n",
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      "Iteration: 1970, Cost function: 3.52506\n",
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      "Iteration: 1972, Cost function: 3.52293\n",
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      "Iteration: 1974, Cost function: 3.52071\n",
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      "Iteration: 1975, Cost function: 3.51964\n",
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      "Iteration: 1979, Cost function: 3.51539\n",
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      "Iteration: 1980, Cost function: 3.51432\n",
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      "Iteration: 1981, Cost function: 3.51326\n",
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      "Iteration: 1982, Cost function: 3.51217\n",
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      "Iteration: 1985, Cost function: 3.50898\n",
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      "Iteration: 1988, Cost function: 3.50589\n",
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      "Iteration: 1989, Cost function: 3.50498\n",
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      "Iteration: 1990, Cost function: 3.50400\n",
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      "Iteration: 1991, Cost function: 3.50306\n",
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      "Iteration: 1992, Cost function: 3.50211\n",
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      "Iteration: 1993, Cost function: 3.50108\n",
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      "Iteration: 1994, Cost function: 3.50012\n",
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      "Iteration: 1995, Cost function: 3.49907\n",
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      "Iteration: 1996, Cost function: 3.49815\n",
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      "Iteration: 1997, Cost function: 3.49712\n",
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      "ADMM_Elapsed Time: 0.073\n",
      "Iteration: 1998, Cost function: 3.49610\n",
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      "Iteration: 1999, Cost function: 3.49513\n",
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      "Time elapsed:  657.9835591316223\n"
     ]
    }
   ],
   "source": [
    "from PIL import Image\n",
    "\n",
    "x_im_L = np.reshape(x_DL_SOM,[L1,L1])\n",
    "x_DL_L_real = np.asarray(Image.fromarray(np.real(x_im_L)).resize((L,L)))\n",
    "x_DL_L_imag = np.asarray(Image.fromarray(np.imag(x_im_L)).resize((L,L)))\n",
    "x_DL_L = np.reshape(x_DL_L_real + 1j*x_DL_L_imag,[L*L,1])\n",
    "w_DL_L = np.zeros([L*L,V],dtype=np.complex128)\n",
    "\n",
    "_, w_DL_L = util_cgfft.cg_fft_forward_problem(x_DL_L, G_S, g_D_fft, e, 1e-3, np.zeros([L*L,V]), 1000)\n",
    "\n",
    "# Use the output of stage IV as inputs for Stage V\n",
    "x_L, _, cost_list_DL = TSOM_withCGFFT_TV(y, G_S, G_D, g_D_fft, g_D_fft_conj, e, w_DL_L, x_DL_L, True, 500, 2000, 25, 1e-4)\n",
    "x_L = np.real(x_L)*(np.real(x_L) >= 0) + 1j*np.imag(x_L)*(np.imag(x_L) <= 0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0xf1e7334e0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display Reconstruction of Austria Profile\n",
    "plt.subplot(3,1,1)\n",
    "plt.imshow(np.real(np.reshape(x_L2,[L,L])))\n",
    "plt.xticks([L*0.25, L*0.5, L*0.75], [-0.5, 0, 0.5],fontsize = '12')\n",
    "plt.yticks([L*0.25, L*0.5, L*0.75], [-0.5, 0, 0.5],fontsize = '12')\n",
    "plt.xlabel('x (in m)', fontsize='16')\n",
    "plt.ylabel('y (in m)', fontsize='16')\n",
    "plt.title('Reconstruction using TSOM-TV', fontsize='18')\n",
    "plt.colorbar()\n",
    "\n",
    "\n",
    "plt.subplot(3,1,3)\n",
    "plt.imshow(np.real(np.reshape(x_L,[L,L])))\n",
    "plt.xticks([L*0.25, L*0.5, L*0.75], [-0.5, 0, 0.5],fontsize = '12')\n",
    "plt.yticks([L*0.25, L*0.5, L*0.75], [-0.5, 0, 0.5],fontsize = '12')\n",
    "plt.xlabel('x (in m)', fontsize='12')\n",
    "plt.ylabel('y (in m)', fontsize='12')\n",
    "plt.title('Reconstruction using Proposed scheme (CS-Net + TSOM-TV)', fontsize='18')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
